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The correction term in a small-ball probability factorization for random curves

Author

Listed:
  • Aubin, Jean-Baptiste
  • Bongiorno, Enea G.
  • Goia, Aldo

Abstract

This work proposes an analysis of the correction term appearing in a Small-Ball Probability factorization for random elements taking values in a separable Hilbert space. Its local nature, its meaning and behavior are discussed also through the derivation of some bounds. Nonparametric kernel-type estimators of the considered statistics are introduced and some asymptotic properties are provided. Finally, in the context of reconstructing a sample of curves by truncated Karhunen–Loève expansion, a local approach to select the dimensionality is illustrated through numerical and real data examples.

Suggested Citation

  • Aubin, Jean-Baptiste & Bongiorno, Enea G. & Goia, Aldo, 2022. "The correction term in a small-ball probability factorization for random curves," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x2100169x
    DOI: 10.1016/j.jmva.2021.104891
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    References listed on IDEAS

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    1. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.
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    6. Th. Gasser & P. Hall & B. Presnell, 1998. "Nonparametric estimation of the mode of a distribution of random curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 681-691.
    7. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    8. Frédéric Ferraty & Nadia Kudraszow & Philippe Vieu, 2012. "Nonparametric estimation of a surrogate density function in infinite-dimensional spaces," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 447-464.
    9. Enea G. Bongiorno & Aldo Goia & Philippe Vieu, 2019. "Modeling functional data: a test procedure," Computational Statistics, Springer, vol. 34(2), pages 451-468, June.
    10. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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